Features of heavy physics in the CMB power spectrum

TL;DR

This work demonstrates that heavy degrees of freedom need not decouple during multi-field inflation when the inflaton follows a curved trajectory in field space. The authors develop a geometric perturbation framework that handles derivative couplings between adiabatic and heavy modes, derive a two-field perturbation system, and construct an effective theory for the adiabatic mode when the transverse mass is large. They show that turning suppresses or enhances power spectrum features and induces a reduced speed of sound, leading to possible correlated non-Gaussian signatures, particularly for localized turns. The results provide a general, nonperturbative approach to predict damped oscillatory features in the CMB power spectrum and outline conditions under which heavy physics can leave observable imprints.

Abstract

The computation of the primordial power spectrum in multi-field inflation models requires us to correctly account for all relevant interactions between adiabatic and non-adiabatic modes around and after horizon crossing. One specific complication arises from derivative interactions induced by the curvilinear trajectory of the inflaton in a multi-dimensional field space. In this work we compute the power spectrum in general multi-field models and show that certain inflaton trajectories may lead to observationally significant imprints of `heavy' physics in the primordial power spectrum if the inflaton trajectory turns, that is, traverses a bend, sufficiently fast (without interrupting slow roll), even in cases where the normal modes have masses approaching the cutoff of our theory. We emphasise that turning is defined with respect to the geodesics of the sigma model metric, irrespective of whether this is canonical or non-trivial. The imprints generically take the form of damped superimposed oscillations on the power spectrum. In the particular case of two-field models, if one of the fields is sufficiently massive compared to the scale of inflation, we are able to compute an effective low energy theory for the adiabatic mode encapsulating certain relevant operators of the full multi-field dynamics. As expected, a particular characteristic of this effective theory is a modified speed of sound for the adiabatic mode which is a functional of the background inflaton trajectory and the turns traversed during inflation. Hence in addition, we expect non-Gaussian signatures directly related to the features imprinted in the power spectrum.

Figures (6)

• Figure 1: A generic example of a potential where turns happens while one of the fields remain much heavier than the other.
• Figure 2: The figure shows schematically the relation between the tangent vector $T^a$, the normal vector $N^a$ and the radius of curvature $\kappa$.
• Figure 3: The figure shows a fixed right-handed orientation of $N^a$ with respect to $T^a$. If the turn is towards the left then $\eta_{\bot}$ is negative, whereas if the turn is towards the right then $\eta_{\bot}$ is positive.
• Figure 4: The figure shows a prototype example of a trajectory which suffers a localised bend towards the right.
• Figure 5: The primordial power spectrum ${\cal P}_{\mathcal{R}}(k)$ normalised in units of $2.46 \times 10^{-9}$, obtained for six different choices of $\Delta N$, $\eta_{\bot {\rm max}}$ and $M^2$. The plots show a comparison between the power spectrum obtained using the full system of equations (solid line) and the one obtained using the effective theory (dashed line). We have chosen as a pivot scale the value $k_{*} = 0.002$Mpc$^{-1}$.